Question

use pascals triangle to expand ((m + 4)^4). ((m + 4)^4 = square)

Explanation:

Step1: Get Pascal's coefficients

For exponent $n=4$, coefficients are $1, 4, 6, 4, 1$.

Step2: Apply binomial expansion formula

Use $(a+b)^n = \sum_{k=0}^n \binom{n}{k}a^{n-k}b^k$, where $a=m$, $b=4$, $n=4$.
First term: $1 \cdot m^4 \cdot 4^0 = m^4$
Second term: $4 \cdot m^3 \cdot 4^1 = 4m^3 \cdot 4 = 16m^3$
Third term: $6 \cdot m^2 \cdot 4^2 = 6m^2 \cdot 16 = 96m^2$
Fourth term: $4 \cdot m^1 \cdot 4^3 = 4m \cdot 64 = 256m$
Fifth term: $1 \cdot m^0 \cdot 4^4 = 1 \cdot 1 \cdot 256 = 256$

Step3: Sum all expanded terms

Add the calculated terms together.

Answer:

$m^4 + 16m^3 + 96m^2 + 256m + 256$